%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG001-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:04:37 PM UTC 2026
% Result : Unsatisfiable 6.27s 1.49s
% Output : CNFRefutation 6.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 80 ( 41 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 87 ( 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X,Y,W,Z] :
( product(W,Z,Y)
| ~ product(W,Z,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X,Y,U,V] :
( equalish(U,V)
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,plain,
! [Y,W,Z] :
( product(W,Z,Y)
| ! [X] :
( ~ product(W,Z,X)
| ~ equalish(X,Y) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f54,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f56,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f60,plain,
! [U,Z,W] :
( sum(U,Z,W)
| ! [X,V] :
( ~ sum(X,V,W)
| ! [Y] :
( ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f61,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f67,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(X,V3,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f75,plain,
! [U,V] :
( equalish(U,V)
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f76,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f79,plain,
~ product(a,additive_identity,additive_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f80,plain,
! [X0,X1,X2,X3,X4] :
( sum(X1,X3,X4)
| ~ product(X0,X2,X4)
| ~ product(X0,X2,X3)
| ~ product(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f68,f52]) ).
fof(f144,plain,
! [X0] : sum(multiply(X0,additive_identity),multiply(X0,additive_identity),multiply(X0,additive_identity)),
inference(resolution,[status(thm)],[f80,f54]) ).
fof(f229,plain,
! [X0,X1,X2] :
( product(X0,X1,X2)
| ~ equalish(multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f51,f54]) ).
fof(f254,plain,
! [X0,X1] :
( sum(additive_identity,X1,additive_identity)
| ~ sum(X0,X1,X0) ),
inference(resolution,[status(thm)],[f61,f56]) ).
fof(f361,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f76,f52]) ).
fof(f2681,plain,
! [X0] : sum(additive_identity,multiply(X0,additive_identity),additive_identity),
inference(resolution,[status(thm)],[f144,f254]) ).
fof(f2770,plain,
! [X0] : equalish(multiply(X0,additive_identity),additive_identity),
inference(resolution,[status(thm)],[f2681,f361]) ).
fof(f2902,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f2770,f229]) ).
fof(f2926,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f79,f2902]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:09:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 6.27/1.49 % Refutation found
% 6.27/1.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.27/1.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.91/1.51 % Elapsed time: 1.139187 seconds
% 7.91/1.51 % CPU time: 8.553364 seconds
% 7.91/1.51 % Total memory used: 90.501 MB
% 7.91/1.51 % Net memory used: 82.597 MB
%------------------------------------------------------------------------------